The present application generally relates to improving a manufacturing or production environment. More particularly, the present application relates to predicting future values and/or current but not measured values, in time series data that represent conditions of the manufacturing or production environment.
Time series data refers to a sequence of data, which is continuously measured at uniform time intervals. Traditional time series forecasting (i.e., forecasting future values of time series) has been used in business intelligence, weather forecasting, stock market prediction, etc. For example, in demand forecasting, the traditional time series forecasting predicts a quantity of an item that will be sold in a following week given increased sales until a current week. In stock market prediction, given stock prices until today, the traditional time series forecasting predicts stock prices for tomorrow. In weather forecasting, the traditional time series forecasting predicts weather for a next day or may be for an entire following week. However, the farther the traditional time series forecasting predicts, the more the traditional time series forecasting is prone to err.
Traditional time series forecasting uses one or more of: Auto-correlation models and Markovian models. In Auto-correlation models, given time series data x1, x2, . . . , xt, these models attempt to predict a next value xt+1. Auto-correlation models include, but are not limited to: Moving average model, Exponential smoothing model, Phase space reconstruction method, etc. Moving average model computes an average of past m values and reports this average as an estimate of a current value. Exponential smoothing model exponentially weights down values that are farther away in time and reports a result (e.g., average of the weighted-down values) as an estimate. Another model in Auto-correlation models computes a current value in time series data as a function of a finite past along with some white noises. The Phase space reconstruction method assumes that time series data of interest is a one dimensional projection of a system whose true phase space is higher dimensional. This Phase space reconstruction method attempts to reconstruct an original dimension and predict current values of the time series data by building statistical models in this reconstructed dimension. Other models in Auto-correlation models incorporate exogenous variables as a linear combination.
Markovian models construct a stationary distribution over a predefined or automatically deciphered state space (e.g., time series). If a state space (e.g., a time series) is not defined, Markovian models decipher hidden states (e.g., future values of the time series). There are variants of these Markovian models which learn state transitions (e.g., changes in time series) as a function of exogenous variables or input vector (e.g., time series data input), however the transitions learned are still stationary in time. The auto-correlation models do not provide a way of partitioning the state space (e.g., an input time series) and modeling non-linear dependencies of exogenous variables (e.g., parameters not described in the time series data input), while the Markovian models learn stationary distributions over the state space which may not be applicable in drifting systems when trying to predict multiple steps ahead, e.g., predict future values of the time series data input. A drifting system refers to its representative time series data having variations over time. In other words, a behavior of a drifting system cannot be accurately predicted in traditional time series forecasting.